Configuration interaction singles, time-dependent Hartree-Fock, and time-dependent density functional theory for the electronic excited states of extended systems

A general formalism for time-dependent linear response theory is presented within the framework of linear-combination-of-atomic-orbital crystalline or bital theory for the electronic excited states of infinite one-dimensional lattices (polymers). The formalism encompasses those of time-dependent Hart ree-Fock theory (TDHF), time-dependent density functional theory (TDDFT), a nd configuration interaction singles theory (CIS) (as the Tamm-Dancoff appr oximation to TDHF) as particular cases. These single-excitation theories ar e implemented by using a trial-vector algorithm, such that the atomic-orbit al-based two-electron integrals are recomputed as needed and the transforma tion of these integrals from the atomic-orbital basis to the crystalline-or bital basis is avoided. Convergence of the calculated excitation energies w ith respect to the number of unit cells taken into account in the lattice s ummations (N) and the number of wave vector sampling points (K) is studied taking the lowest singlet and triplet exciton states of all-trans polyethyl ene as an example. The CIS and TDHF excitation energies of polyethylene sho w rapid convergence with respect to K and they are substantially smaller th an the corresponding Hartree-Fock fundamental band gaps. In contrast, the e xcitation energies obtained from TDDFT and its modification, the Tamm-Danco ff approximation to TDDFT, show slower convergence with respect to K and th e excitation energies to the lowest singlet exciton states tend to collapse to the corresponding Kohn-Sham fundamental band gaps in the limit of K --> infinity. We consider this to be a consequence of the incomplete cancellati on of the self-interaction energy in the matrix elements of the TDDFT matri x eigenvalue equation, and to be a problem inherent to the current approxim ate exchange-correlation potentials that decay too rapidly in the asymptoti c region. (C) 1999 American Institute of Physics. [S0021- 9606(99)30248-8].